# simplifying trig identity

• Jan 27th 2010, 04:52 PM
Mike Clemmons
simplifying trig identity
Hi. looking for help with simplifying an identity. The identity to be simplified is:
tan^4x + 2tan^2x + 1.

I'm confident that 2tan^2x + 1 will break down into:
tan^2x + tan^2x + 1 which equals tan^2x + sec^2x. But I'm not sure how to treat the tan^4 when converting to secant.

Any help will be much appreciate.
Mike Clemmons
• Jan 27th 2010, 06:34 PM
TheEmptySet
Quote:

Originally Posted by Mike Clemmons
Hi. looking for help with simplifying an identity. The identity to be simplified is:
tan^4x + 2tan^2x + 1.

I'm confident that 2tan^2x + 1 will break down into:
tan^2x + tan^2x + 1 which equals tan^2x + sec^2x. But I'm not sure how to treat the tan^4 when converting to secant.

Any help will be much appreciate.
Mike Clemmons

Note that the problem is in the form

$y^4+2y^2+1=(y^2+1)^2$

where $y=\tan(x)$

This should get you started.
• Jan 27th 2010, 08:36 PM
Prove It
Also recall that $\tan^2{\theta} + 1 = \sec^2{\theta}$.